y^2-20y=20y+100

Solution for y^2-20y=20y+100 equation:

y^2-20y=20y+100

We move all terms to the left:

y^2-20y-(20y+100)=0

We get rid of parentheses

y^2-20y-20y-100=0

We add all the numbers together, and all the variables

y^2-40y-100=0

a = 1; b = -40; c = -100;
Δ = b2-4ac
Δ = -402-4·1·(-100)
Δ = 2000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{5}}{2*1}=\frac{40-20\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{5}}{2*1}=\frac{40+20\sqrt{5}}{2}
$